PSI - Issue 19

Jeroen Van Wittenberghe et al. / Procedia Structural Integrity 19 (2019) 41–48 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4

results in an excitation force with an elliptical shape over a revolution. By changing the phase difference φ between force vectors F 1 and F 2 , the orientation of both the linear or elliptical loading can be controlled. More details and other loading conditions have been published by Van Wittenberghe and Thibaux (2018).

Figure 3: Combined force vectors for the double excenter assembly: a) F 1 = F 2 ; b) F 1 > F 2 .

3. Fatigue testing of large-scale steel structures: 3 cases

3.1. Large-diameter pipe

In this paragraph the directional loading control system is illustrated by test results obtained on the 711mm OD x 25.4mm WT x 9.25m L pipe (see Figure 1), the analytically calculated eigenfrequency for the first bending mode is 29.1 Hz. In Figure 4.a the horizontal and vertical displacements are plotted for contra-rotating excentermasses of equal weight. This results in a linear pipe deflection. The response at 27.50 Hz is plotted for 4 different phase differences ( φ = 0°, 22.5°, 45° and 90°). When an elliptical force vector is applied like schematically shown in Figure 3.b, an elliptical response of the pipe deflection can be observed as shown in Figure 4.b. This plot shows 3 pipe deflections for an excenter combination with 50% compensation ( F 1 = 2· F 2 ). The 3 ellipses correspond to values of the phase difference φ = 0°, 45° and 90°. The elliptical deflection shape is again following the orientation which is controlled by the phase difference φ = 0°, 45° and 90°. When only one excentermass is used, the excitation force is circular, and a circular pipe response can be measured at the center of the pipe (see Figure 3.c). These response graphs illustrate that the general shape of the pipe deflection correspond to the applied excitation force. The loading direction is controlled by the phase difference that can be controlled during a running fatigue test. This allows to either compensate for pipe imperfections such as excentricity and ovality, or to apply non-axisymmetric loads for example to concentrate the loading on a certain location around the circumference or to simulate more realistic loading conditions.

8

8

8

0°

45°

0°

22.5°

6

6

6

90°

45°

90°

4

4

4

2

2

2

0

0

0

-2

-2

-2

-4

-4

-4

Vertical Displacement [mm]

-6

-6 Vertical Displacement [mm]

-6 Vertical Displacement [mm]

-8

-8

-8

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

-8 -6 -4 -2 0 2 4 6 8

Horizontal Displacement [mm]

Horizontal Displacement [mm]

Horizontal Displacement [mm]

a) c) Figure 4: XY-plot at 27.50 Hz for different phase differences for a) F 1 = F 2 , b) F 1 = 2· F 2 . The circular response is obtained with a single excentermass and plotted for a frequency of 28.00 Hz. b)